If you want to use a variable number of keyed elements with dynamically generated keys, instead of creating variables with dynamically generated names (it's not really possible, it is possible to create classes with dynamically generated elements but requires tons of hacking), just use a plain old Map:

Map<String, File> myFiles = new HashMap<>();

Then, you can do:

myFiles.put("fileName" + i, file);

EDIT: then, for your postulated problem, you can do:

for (File file : myFiles.values()) {
if (file.exists()) { ... }
}

If the keys don't matter, you can even use a normal List instead of a Map.